. hho be means of examples that union of t o subgroups may or may not be subgroups

It seems like you're asking for examples to illustrate when the union of two subgroups is or is not a subgroup itself. Here are two examples:

1. Union of Two Subgroups is NOT a Subgroup:

Consider two subgroups H and K of a group G. Let's say H = {e, a} and K = {e, b} where e is the identity, a and b are elements of G. The union of H and K is {e, a, b}. This set is not a subgroup of G because it's not closed under the operation of the group. For instance, if the operation is multiplication, then a*b is not in {e, a, b}.

2. Union of Two Subgroups is a Subgroup:

This is only possible if one subgroup is contained within the other. For example, let H = {e, a} and K = {e, a, b} be subgroups of a group G. The union of H and K is K itself, {e, a, b}, which is a subgroup of G.

So, the union of two subgroups is a subgroup if and only if one subgroup is a subset of the other.